Our calculation of the state space curvature can be contrasted with those of  [1]}, [2]}, [3]} and especially  [4]}, [5]}. In these studies, it is the curvature corresponding to the ground state manifold parameterized by the driving parameters of the phase transitions themselves that is computed. In particular,  [4]} finds that the curvature of the manifold parameterized by a uniform field along the \(z\)  axis and the temperature in the XXZ model reveal different scaling regimes in the vicinity of the quantum critical point.
